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PostPosted: Tue, 8 May 2012 17:21:29 UTC 
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----The random variables X and Y are N(0,2) (Normal or Gaussian distributed) and independent. Find the PDF and CDF of Z = 2X + 3Y.


-------Two fair dice are rolled. Find the joint probability mass function of X and Y when X is the largest value obtained on any die and Y is the sum of the values.


------Given the joint PMF of X and Y as
Px,y(x,y)=
{1/4 (x,y)=(1,1) }
{1/4 (x,y)=(-1,1) }
{1/2 (x,y)=(0,0) }
{ 0 otherwise }
(a) Find E[X], E[Y], and E[XY],
(b) Show that X and Y are uncorrelated,
(c) Determine if X and Y are independent or not.


-------The joint density function of X and Y is
Fx,y(x,y)=
{ x+y 0<x<1.0<y<1
0 otherwise }

a) Are X and Y independent?
b) Find the density function of X?
c) Find P(X+Y < 1)=?

------Suppose the joint density function of X and Y is given by

Fx,y(x,y)=
{((e^-x/y) * (e^-y))/y 0<x<oo , 0<y<oo
0 otherwise }

a) Find the conditional density of x, given that Y=y.
b) Find P(X > 1 | Y = y).


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PostPosted: Tue, 8 May 2012 17:42:01 UTC 
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Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
Where is(are) your attempt(s)?

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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PostPosted: Tue, 8 May 2012 17:47:15 UTC 
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PostPosted: Tue, 8 May 2012 19:09:57 UTC 
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We can't help you if you don't show your work...

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